Presumptive Democratic nominee Hillary Clinton also has historically high unfavorability ratings, but with CNN hosting a town hall with the Libertarian Party ticket of Gary Johnson and William Weld Wednesday, the focus is on disaffected conservatives for the moment.

Robert Bentley, a history and political science professor from Colorado, says he has always been a libertarian at heart. “But I officially changed my party from Republican [to Libertarian] back in February.”

“We can no longer be Republicans. [Mr. Trump] sparked the exodus of me and others away from the party,” adds Professor Bentley. “I thought I may as well go ahead and register with [the Libertarians] now.”

In the grand sweep of American two-party politics, the numbers are small. But they are big enough to be potentially significant – especially if they continue to grow.

In a CNN poll last week, one-third of undecided voters said they would choose Libertarian nominee Mr. Johnson over Mrs. Clinton or Trump. Some 9 percent of voters said they would choose Johnson if he was featured on a four-way ticket with Clinton, Trump, and Jill Stein of the Green Party.

If public support rises to 15 percent, Johnson will be included in primetime presidential debates this fall. And support is rising at record-breaking levels – at least for the scrappy party.

Nationwide, the 5,000 new members since January represent a historic number, says Wes Benedict, executive director of the Libertarian Party. In Massachusetts, the state party has seen a three-fold increase in donations and a four-fold increase in volunteers, also breaking previous records, says state chairman George Phillies.

The party will still have to clear the same hurdles that have long stymied third parties: lack of fundraising and media attention. While Clinton may raise $1 billion, Johnson will struggle to raise even $10 million.

But it is unquestionably a moment for the Libertarians.

“What the Libertarian Party didn’t have until now was deep dissatisfaction with the major party candidates and a presidential ticket that was plausible – looked like someone you could vote for,” says David Boaz, Executive Vice President at the Cato Institute. “It’s unparalleled in the history of third party candidacy.”

Libertarians themselves embrace political refugees from the major parties.

“That undeniably has an impact and is giving voters a reason to look for a viable third option,” says Joe Hunter, director of communications for presidential nominee Johnson and vice presidential nominee Mr. Weld.

But Mr. Hunter notes that the party has taken full advantage. In a race where the presumed Republican nominee has no political experience, the Libertarians are featuring a ticket with two two-term governors who served as Republicans in blue states: Johnson in New Mexico and Weld in Massachusetts.

The “third option must be a credible one, and two successful governors are obviously credible,” adds Mr. Hunter.

This election is simply allowing people who have long leaned libertarian to call themselves Libertarians, suggest Mr. Phillies of the Massachusetts branch.

Some of the new recruits agree.

“I got one of those quizzes on social media that said, ‘We’ll tell you who to vote for’ back in 2012. And I talked to a lot of people, both Republicans and Democrats, and we all got the same answer: Gary Johnson is your guy,” says Bryan Stone, a radio talk show host from Tennessee. “Now I’m going back to that poll four years ago. These are the two worst candidates in the history of American politics – [Johnson] seems like the most logical avenue.”

Others say they have taken a similar journey to the Libertarian Party.

“I was a Republican all my life, but the last three to four years I started leaning toward Libertarian. And this election cycle has really pushed me over the edge,” adds Brett Hamilton, a construction worker from Texas.

Speaking of the people he works with, he adds, “For whatever reason, they just don’t like Donald Trump and they’ll be damned if they vote for Hillary.”

The Libertarian Party currently has its candidates on the ballot in 33 states. But Libertarian Party leaders say they expect to be on the ballot in all 50 states by November.

For Libertarians, the hope is that their new members will stay.

“A lot of people are taking a look at the Libertarian party because they don’t like Donald Trump or Hillary Clinton,” says Mr. Benedict, the executive director. “But once they come here and see what we’re about, they like what they see. It will take a year or two to find out if they’ll stay, but people see us and say ‘Hey, that’s what I am: fiscally conservative and socially tolerant.’ ”

“The Libertarian Party has been given the stage,” adds Mr. Boaz of the Cato Institute, “and now it is their job to make a good show.”